Event included


An event included in another is one whose occurrence also implies the occurrence of another event in which it is included.

The mathematical way to denote an included event is by the sign ⊂. That sign means included. Thus, given an event A and another event B, we will notice that A is included in B as follows:


The intuitive way to read the above would be:

"A is included in B if whenever A occurs, B also occurs."

The reverse of this statement is not true.

Venn diagram of event included

An included event is represented graphically as:

How can we check, event B (circle B) is bigger. It contains some results and within these results is the event A (circle A). Next, we will show an example.

Event example included

Following the same structure of the image in the previous example, we are going to explain the concept. We will do it in a simple way.

Suppose we are at the toss of a six-sided die. Each face contains a number. Thus, the possible outcomes are {1,2,3,4,5,6}

Event A will be exit even. And, event B, will be exit 4. In such a way that the thing would be like this:

Event A: {2,4,6}

Event B: {4}

Therefore, whenever event A occurs (with a 4), event B will also occur (with an even number). Now, the occurrence of event B (exit even) does not imply that event A (exit 4) occurs. This is so, because if a 2 comes out, B would be happening, but not A.

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